The Maryland model describes particles hopping in a tight-binding
lattice and subject to an unbounded onsite superlattice potential.
Its Hamiltonian in position representation takes the form \(H_{0}=\sum _{n}(J|n\rangle \langle n+1|+{\rm H.c.}+V\tan (\pi \alpha n)|n\rangle \langle n|)\) .
Here \(J\)  is the nearest-neighbor (NN) hopping amplitude, \(V\)  is the amplitude
of onsite potential, \(n\in \mathbb {Z}\)  is the lattice site index and
\(\lbrace |n\rangle \rbrace \)  forms a complete basis of the lattice. \(\alpha \) 
is chosen as an irrational number to realize quasiperiodic
modulations. The Hermitian Maryland model \(H_{0}\)  is first
introduced as an integrable model to study localization problems in
quantum chaotic systems [1]}, [2]}, [3]}, [4]}, [5]}, [6]}. Later, it
is also utilized to understand the localization in higher dimensions [7]}, [8]}, [9]}
and topological features of integer quantum Hall
effects [10]}. Experimentally, the Maryland model might be
realized in photonic systems by engineering the light propagation
in polygonal optical waveguide lattices [11]}.
